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Results (displaying all 20 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.4.287109855921268900000000.3	x¹⁶ - x¹⁵ - 6x¹⁴ - 8x¹³ - 8x¹² - 25x¹¹ - 194x¹⁰ - 172x⁹ + 25x⁸ + 1214x⁷ + 1538x⁶ - 384x⁵ - 740x⁴ - 5248x³ + 1752x² - 976x + 4496	$ 2^{8}\cdot 5^{8}\cdot 13^{6}\cdot 29^{6} $	16T1191	$[2]$
16.4.287109855921268900000000.4	x¹⁶ - x¹⁵ - 5x¹⁴ + 30x¹³ - 25x¹² - 88x¹¹ + 237x¹⁰ - 377x⁹ - 143x⁸ + 941x⁷ - 322x⁶ + 118x⁵ - 1109x⁴ + 1968x³ - 1531x² - 1056x + 941	$ 2^{8}\cdot 5^{8}\cdot 13^{6}\cdot 29^{6} $	16T1191	Trivial
16.4.454534084285444900000000.1	x¹⁶ - 7x¹⁵ + 33x¹⁴ - 113x¹³ + 286x¹² - 647x¹¹ + 1110x¹⁰ - 1814x⁹ + 2773x⁸ - 3492x⁷ + 5639x⁶ - 1104x⁵ + 1031x⁴ + 11562x³ - 33080x² + 22975x - 93649	$ 2^{8}\cdot 5^{8}\cdot 11^{6}\cdot 37^{6} $	16T1191	Trivial (GRH)
16.4.454534084285444900000000.2	x¹⁶ - x¹⁵ - 17x¹³ - 35x¹² - 11x¹¹ + 51x¹⁰ + 142x⁹ + 418x⁸ + 1126x⁷ + 2859x⁶ + 1798x⁵ + 55x⁴ + 474x³ - 505x² - 247x + 361	$ 2^{8}\cdot 5^{8}\cdot 11^{6}\cdot 37^{6} $	16T1191	Trivial (GRH)
16.0.473832177901327746072576.1	x¹⁶ - 2x¹⁴ + 54x¹² - 84x¹⁰ + 2159x⁸ + 3696x⁶ + 33630x⁴ + 72270x² + 47961	$ 2^{32}\cdot 3^{6}\cdot 73^{6} $	16T1191	Trivial (GRH)
16.0.473832177901327746072576.2	x¹⁶ - 16x¹⁴ + 106x¹² - 482x¹⁰ + 2480x⁸ - 11850x⁶ + 36183x⁴ - 61758x² + 47961	$ 2^{32}\cdot 3^{6}\cdot 73^{6} $	16T1191	Trivial (GRH)
16.4.1791497443643622400000000.2	x¹⁶ - 4x¹⁴ + 20x¹² - 369x¹⁰ + 52x⁸ + 6636x⁶ - 7602x⁴ - 26999x² + 41209	$ 2^{16}\cdot 5^{8}\cdot 7^{6}\cdot 29^{6} $	16T1191	Trivial (GRH)
16.4.1791497443643622400000000.3	x¹⁶ + 4x¹⁴ + 20x¹² + 369x¹⁰ + 52x⁸ - 6636x⁶ - 7602x⁴ + 26999x² + 41209	$ 2^{16}\cdot 5^{8}\cdot 7^{6}\cdot 29^{6} $	16T1191	Trivial (GRH)
16.0.2838932997008222500000000.1	x¹⁶ - 7x¹⁵ + 16x¹⁴ - 14x¹³ + 69x¹² - 142x¹¹ - 466x¹⁰ + 1197x⁹ + 1315x⁸ - 3872x⁷ - 954x⁶ + 3860x⁵ + 3196x⁴ + 2744x³ - 8776x² - 10880x + 13264	$ 2^{8}\cdot 5^{10}\cdot 17^{6}\cdot 19^{6} $	16T1191	$[2]$
16.0.2838932997008222500000000.2	x¹⁶ + 16x¹⁴ - 20x¹³ + 101x¹² - 66x¹¹ + 678x¹⁰ + 691x⁹ + 4700x⁸ + 5336x⁷ + 15655x⁶ + 8198x⁵ + 20962x⁴ + 345x³ + 2282x² - 19x + 71	$ 2^{8}\cdot 5^{10}\cdot 17^{6}\cdot 19^{6} $	16T1191	$[2]$
16.4.116360725577073894400000000.1	x¹⁶ - 40x¹² - 46x⁸ + 2035x⁴ + 165649	$ 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 37^{6} $	16T1191	Trivial (GRH)
16.4.116360725577073894400000000.2	x¹⁶ + 25x¹² + 509x⁸ - 26455x⁴ + 165649	$ 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 37^{6} $	16T1191	$[2]$ (GRH)
16.0.512375501660226220900000000.1	x¹⁶ - 4x¹⁵ + 20x¹⁴ - 37x¹³ + 110x¹² - 152x¹¹ - 421x¹⁰ + 4047x⁹ - 5496x⁸ - 3183x⁷ + 46778x⁶ - 13463x⁵ + 29324x⁴ + 59277x³ + 13479x² - 2645x + 445	$ 2^{8}\cdot 5^{8}\cdot 13^{6}\cdot 101^{6} $	16T1191	$[2, 2]$ (GRH)
16.0.512375501660226220900000000.2	x¹⁶ - x¹⁵ + 27x¹⁴ + 22x¹³ + 347x¹² + 792x¹¹ + 3553x¹⁰ + 8941x⁹ + 26087x⁸ + 53761x⁷ + 108800x⁶ + 173586x⁵ + 246251x⁴ + 258392x³ + 202021x² + 96070x + 19195	$ 2^{8}\cdot 5^{8}\cdot 13^{6}\cdot 101^{6} $	16T1191	$[2, 2]$ (GRH)
16.8.117407576466628437606400000000.5	x¹⁶ - 12x¹⁴ - 449x¹² + 7016x¹⁰ - 6490x⁸ - 134386x⁶ - 134386x⁴ + 82418x² + 41209	$ 2^{32}\cdot 5^{8}\cdot 7^{6}\cdot 29^{6} $	16T1191	Trivial (GRH)
16.8.117407576466628437606400000000.6	x¹⁶ - 4x¹⁴ - 202x¹² + 1472x¹⁰ + 1350x⁸ - 21672x⁶ + 497x⁴ + 71050x² + 41209	$ 2^{32}\cdot 5^{8}\cdot 7^{6}\cdot 29^{6} $	16T1191	Trivial (GRH)
16.0.215429589500286246610837301474983006961664.3	x¹⁶ + 1336x¹⁴ + 723214x¹² + 202880976x¹⁰ + 31228142425x⁸ + 2556746204384x⁶ + 97478917371936x⁴ + 1157359870269768x² + 4107750751677169	$ 2^{48}\cdot 3^{8}\cdot 73^{6}\cdot 937^{4} $	16T1191	$[2, 2, 2, 2, 2, 67083750]$ (GRH)
16.16.215429589500286246610837301474983006961664.3	x¹⁶ - 1816x¹⁴ + 1120320x¹² - 323759520x¹⁰ + 48091401945x⁸ - 3668323194472x⁶ + 133470657752078x⁴ - 1858790094675688x² + 4107750751677169	$ 2^{48}\cdot 3^{8}\cdot 73^{6}\cdot 937^{4} $	16T1191	$[2]$ (GRH)
16.0.215429589500286246610837301474983006961664.4	x¹⁶ + 1816x¹⁴ + 1120320x¹² + 323759520x¹⁰ + 48091401945x⁸ + 3668323194472x⁶ + 133470657752078x⁴ + 1858790094675688x² + 4107750751677169	$ 2^{48}\cdot 3^{8}\cdot 73^{6}\cdot 937^{4} $	16T1191	$[2, 2, 2, 2, 2, 73397938]$ (GRH)
16.16.215429589500286246610837301474983006961664.4	x¹⁶ - 1336x¹⁴ + 723214x¹² - 202880976x¹⁰ + 31228142425x⁸ - 2556746204384x⁶ + 97478917371936x⁴ - 1157359870269768x² + 4107750751677169	$ 2^{48}\cdot 3^{8}\cdot 73^{6}\cdot 937^{4} $	16T1191	$[2]$ (GRH)

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	Polynomial	Discriminant	Galois group	Class group
16.4.287109855921268900000000.3	x¹⁶ - x¹⁵ - 6x¹⁴ - 8x¹³ - 8x¹² - 25x¹¹ - 194x¹⁰ - 172x⁹ + 25x⁸ + 1214x⁷ + 1538x⁶ - 384x⁵ - 740x⁴ - 5248x³ + 1752x² - 976x + 4496	\( 2^{8}\cdot 5^{8}\cdot 13^{6}\cdot 29^{6} \)	16T1191	$[2]$
16.4.287109855921268900000000.4	x¹⁶ - x¹⁵ - 5x¹⁴ + 30x¹³ - 25x¹² - 88x¹¹ + 237x¹⁰ - 377x⁹ - 143x⁸ + 941x⁷ - 322x⁶ + 118x⁵ - 1109x⁴ + 1968x³ - 1531x² - 1056x + 941	\( 2^{8}\cdot 5^{8}\cdot 13^{6}\cdot 29^{6} \)	16T1191	Trivial
16.4.454534084285444900000000.1	x¹⁶ - 7x¹⁵ + 33x¹⁴ - 113x¹³ + 286x¹² - 647x¹¹ + 1110x¹⁰ - 1814x⁹ + 2773x⁸ - 3492x⁷ + 5639x⁶ - 1104x⁵ + 1031x⁴ + 11562x³ - 33080x² + 22975x - 93649	\( 2^{8}\cdot 5^{8}\cdot 11^{6}\cdot 37^{6} \)	16T1191	Trivial (GRH)
16.4.454534084285444900000000.2	x¹⁶ - x¹⁵ - 17x¹³ - 35x¹² - 11x¹¹ + 51x¹⁰ + 142x⁹ + 418x⁸ + 1126x⁷ + 2859x⁶ + 1798x⁵ + 55x⁴ + 474x³ - 505x² - 247x + 361	\( 2^{8}\cdot 5^{8}\cdot 11^{6}\cdot 37^{6} \)	16T1191	Trivial (GRH)
16.0.473832177901327746072576.1	x¹⁶ - 2x¹⁴ + 54x¹² - 84x¹⁰ + 2159x⁸ + 3696x⁶ + 33630x⁴ + 72270x² + 47961	\( 2^{32}\cdot 3^{6}\cdot 73^{6} \)	16T1191	Trivial (GRH)
16.0.473832177901327746072576.2	x¹⁶ - 16x¹⁴ + 106x¹² - 482x¹⁰ + 2480x⁸ - 11850x⁶ + 36183x⁴ - 61758x² + 47961	\( 2^{32}\cdot 3^{6}\cdot 73^{6} \)	16T1191	Trivial (GRH)
16.4.1791497443643622400000000.2	x¹⁶ - 4x¹⁴ + 20x¹² - 369x¹⁰ + 52x⁸ + 6636x⁶ - 7602x⁴ - 26999x² + 41209	\( 2^{16}\cdot 5^{8}\cdot 7^{6}\cdot 29^{6} \)	16T1191	Trivial (GRH)
16.4.1791497443643622400000000.3	x¹⁶ + 4x¹⁴ + 20x¹² + 369x¹⁰ + 52x⁸ - 6636x⁶ - 7602x⁴ + 26999x² + 41209	\( 2^{16}\cdot 5^{8}\cdot 7^{6}\cdot 29^{6} \)	16T1191	Trivial (GRH)
16.0.2838932997008222500000000.1	x¹⁶ - 7x¹⁵ + 16x¹⁴ - 14x¹³ + 69x¹² - 142x¹¹ - 466x¹⁰ + 1197x⁹ + 1315x⁸ - 3872x⁷ - 954x⁶ + 3860x⁵ + 3196x⁴ + 2744x³ - 8776x² - 10880x + 13264	\( 2^{8}\cdot 5^{10}\cdot 17^{6}\cdot 19^{6} \)	16T1191	$[2]$
16.0.2838932997008222500000000.2	x¹⁶ + 16x¹⁴ - 20x¹³ + 101x¹² - 66x¹¹ + 678x¹⁰ + 691x⁹ + 4700x⁸ + 5336x⁷ + 15655x⁶ + 8198x⁵ + 20962x⁴ + 345x³ + 2282x² - 19x + 71	\( 2^{8}\cdot 5^{10}\cdot 17^{6}\cdot 19^{6} \)	16T1191	$[2]$
16.4.116360725577073894400000000.1	x¹⁶ - 40x¹² - 46x⁸ + 2035x⁴ + 165649	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 37^{6} \)	16T1191	Trivial (GRH)
16.4.116360725577073894400000000.2	x¹⁶ + 25x¹² + 509x⁸ - 26455x⁴ + 165649	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 37^{6} \)	16T1191	$[2]$ (GRH)
16.0.512375501660226220900000000.1	x¹⁶ - 4x¹⁵ + 20x¹⁴ - 37x¹³ + 110x¹² - 152x¹¹ - 421x¹⁰ + 4047x⁹ - 5496x⁸ - 3183x⁷ + 46778x⁶ - 13463x⁵ + 29324x⁴ + 59277x³ + 13479x² - 2645x + 445	\( 2^{8}\cdot 5^{8}\cdot 13^{6}\cdot 101^{6} \)	16T1191	$[2, 2]$ (GRH)
16.0.512375501660226220900000000.2	x¹⁶ - x¹⁵ + 27x¹⁴ + 22x¹³ + 347x¹² + 792x¹¹ + 3553x¹⁰ + 8941x⁹ + 26087x⁸ + 53761x⁷ + 108800x⁶ + 173586x⁵ + 246251x⁴ + 258392x³ + 202021x² + 96070x + 19195	\( 2^{8}\cdot 5^{8}\cdot 13^{6}\cdot 101^{6} \)	16T1191	$[2, 2]$ (GRH)
16.8.117407576466628437606400000000.5	x¹⁶ - 12x¹⁴ - 449x¹² + 7016x¹⁰ - 6490x⁸ - 134386x⁶ - 134386x⁴ + 82418x² + 41209	\( 2^{32}\cdot 5^{8}\cdot 7^{6}\cdot 29^{6} \)	16T1191	Trivial (GRH)
16.8.117407576466628437606400000000.6	x¹⁶ - 4x¹⁴ - 202x¹² + 1472x¹⁰ + 1350x⁸ - 21672x⁶ + 497x⁴ + 71050x² + 41209	\( 2^{32}\cdot 5^{8}\cdot 7^{6}\cdot 29^{6} \)	16T1191	Trivial (GRH)
16.0.215429589500286246610837301474983006961664.3	x¹⁶ + 1336x¹⁴ + 723214x¹² + 202880976x¹⁰ + 31228142425x⁸ + 2556746204384x⁶ + 97478917371936x⁴ + 1157359870269768x² + 4107750751677169	\( 2^{48}\cdot 3^{8}\cdot 73^{6}\cdot 937^{4} \)	16T1191	$[2, 2, 2, 2, 2, 67083750]$ (GRH)
16.16.215429589500286246610837301474983006961664.3	x¹⁶ - 1816x¹⁴ + 1120320x¹² - 323759520x¹⁰ + 48091401945x⁸ - 3668323194472x⁶ + 133470657752078x⁴ - 1858790094675688x² + 4107750751677169	\( 2^{48}\cdot 3^{8}\cdot 73^{6}\cdot 937^{4} \)	16T1191	$[2]$ (GRH)
16.0.215429589500286246610837301474983006961664.4	x¹⁶ + 1816x¹⁴ + 1120320x¹² + 323759520x¹⁰ + 48091401945x⁸ + 3668323194472x⁶ + 133470657752078x⁴ + 1858790094675688x² + 4107750751677169	\( 2^{48}\cdot 3^{8}\cdot 73^{6}\cdot 937^{4} \)	16T1191	$[2, 2, 2, 2, 2, 73397938]$ (GRH)
16.16.215429589500286246610837301474983006961664.4	x¹⁶ - 1336x¹⁴ + 723214x¹² - 202880976x¹⁰ + 31228142425x⁸ - 2556746204384x⁶ + 97478917371936x⁴ - 1157359870269768x² + 4107750751677169	\( 2^{48}\cdot 3^{8}\cdot 73^{6}\cdot 937^{4} \)	16T1191	$[2]$ (GRH)